Snap or project bezier curve to mesh surface
I won't mark it as answered because maybe there are some other ways to achieve this which are more accurate.
My solution finally has been to try different modes on the Shrinkwrap modifier (mostly Project and Closest points, with Outside surface option selected), and moving the curve until I get something close to what I need.
Once got that, I would Convert to Mesh (it will apply the modifier, to avoid final shape to be distorted because there are not enough points). Here I had sometimes to use another Shrinkwrap modifier again just to solve some missalignments, and Convert to Curve.
Finally, for the latest adjustments, just turn on the Snap feature with Snap to faces and isolate the objects so the only visible objects are the curve and the mesh you want to snap it to. Enter edit mode with the curve selected and move the unaligned points so that they stick in the surface of the mesh.
They seem a lot of steps, but they're pretty straightforward and quick to do once you get it.
To sum up:

Shrinkwrap modifier until you get close to what you'd like
Convert to Mesh
Apply another Shrinkwrap modifier if needed
Convert to Curve
Hide everything except mesh and curve
Activate Snap feature, with Snap to face
Select the curve and enter edit mode, and move the unaligned points

Don't forget to Apply all transforms when you're done!